Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace

TL;DR

This paper develops a framework using Drinfeld twists to restore supersymmetry in non-anticommutative superspace theories, preserving key structures and identities despite supersymmetry breaking.

Contribution

It introduces a Drinfeld-twisted Hopf superalgebra approach to maintain twisted supersymmetry in non-anticommutative superspace field theories.

Findings

Restores twisted supersymmetry in deformed superspace

Preserves representation content of undeformed theories

Discusses implications for non-renormalization theorems

Abstract

We extend the analysis of hep-th/0408069 on a Lorentz invariant interpretation of noncommutative spacetime to field theories on non-anticommutative superspace with half the supersymmetries broken. By defining a Drinfeld-twisted Hopf superalgebra, it is shown that one can restore twisted supersymmetry and therefore obtain a twisted version of the chiral rings along with certain Ward-Takahashi identities. Moreover, we argue that the representation content of theories on the deformed superspace is identical to that of their undeformed cousins and comment on the consequences of our analysis concerning non-renormalization theorems.